You ran some BBS software on your computer and people could dial in directly to your system and play games, write text messages, etc - they had to know your phone number of course 
Most of the ones I worked with had multiple lines so several people could be on at the same time, a few you had set times you could call in.
Really slow, but was how we did it back then.
From Wiki:
A bulletin board system, or BBS, is a computer system running software that allows users to connect and log into the system using a terminal program. Once logged in, a user can perform functions such as uploading and downloading software and data, reading news and bulletins, and exchanging messages with other users, either through email, public message boards, and sometimes via direct chatting. Many BBSes also offer on-line games, in which users can compete with each other, and BBSes with multiple phone lines often provide chat rooms, allowing users to interact with each other.
Originally BBSes were accessed only over a phone line using a modem, but by the early 1990s some BBSes allowed access via a Telnet, packet switched network, or packet radio connection.
more: http://en.wikipedia.org/wiki/Bulletin_board_system
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